Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C23×C3×D8 ⋊ C2 |
| Sylow | C3 ⋊ #33517 |
1380 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 211 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|e^2=gh,g^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eg,g^a=gh,i^a=i^2,e^b=eg,g^b=gh102 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#33517, #72219843, #72219844 |
| maximal normal subgroup of | D3×#33517, #72219843, #72219844 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323355);